Question: Divide. Write the quotient in lowest terms. $1\dfrac{1}{3} \div 1\dfrac34 = $
Explanation: First, let's rewrite $1\dfrac13$ and $1\dfrac34$ as fractions: $1\dfrac{1}{3} \div 1\dfrac34 =\dfrac{4}3 \div \dfrac74$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac74$ is $\dfrac47$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{4}3 \div \dfrac74=\dfrac43\times\dfrac47$ $=\dfrac{4 \times 4}{3 \times 7}$ $=\dfrac{16}{21}$